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Bharat Institute of Engineering and Technology
Ibrahimpatnam, R R District – 501 506 (Telangana)
Department of Mechanical
Engineering
Lab Manual
KINEMATICS AND DYNAMICS OF MACHINE
INSTITUTE VISION & MISSION
VISION: To achieve the deemed university status and spread universal education by
inculcating discipline, character and knowledge into the young minds and mould them into
enlightened citizens.
MISSION: Our mission is to impart high quality education, in a conductive ambience, as
comprehensive as possible, with the support of all the modern technologies and make the
students acquire the ability and passion to work wisely, creatively and effectively for the
betterment of our society.
DEPARTMENT VISION & MISSION
VISION: The Mechanical Engineering Department strives to be recognized as world class
Institution, by creating centres of excellence in the field of Mechanical Engineering and
promoting Entrepreneurship with Value-based teaching – learning process.
MISSION: The Mechanical Engineering Department strives to impart quality education to
the students and enhancing their skills to make them high quality Mechanical Engineers and
to provide state of art research facilities for the students to enhance their technical knowledge
for the development of industry. Our department tries to link with world class educational
institutions and R&D organizations to excel in research and serve the community.
PROGRAMME EDUCATIONAL OBJECTIVES
Program Educational Objective 1: (PEO1)
Apply technical knowledge and skills as mechanical engineers to provide optimal solutions in
industrial and government organizations.
Program Educational Objective 2: (PEO2)
Pursue advanced education, research and development, and other creative and innovative
efforts in science, engineering, and technology, as well as other professional careers.
Program Educational Objective 3: (PEO3)
Practice professional and ethical responsibilities, including the societal impact of engineering
solutions.
Program Educational Objective 4: (PEO4)
Participate as leaders in their fields of expertise and in activities that support service and
economic development nationally and throughout the world.
PROGRAMME OUTCOMES
PO1: ENGINEERING KNOWLEDGE: Apply the knowledge of mathematics, science, engineering
fundamentals, and an engineering specialization to the solution of complex engineering problems.
PO2: PROBLEM ANALYSIS: Identify, formulate, review research literature, and analyze complex
engineering problems reaching substantiated conclusions using first principles of mathematics, natural sciences,
and engineering sciences.
PO3: DESIGN/DEVELOPMENT OF SOLUTIONS: Design solutions for complex engineering problems
and design system components or processes that meet the specified needs with appropriate consideration for the
public health and safety, and the cultural, societal, and environmental considerations.
PO4: CONDUCT INVESTIGATIONS OF COMPLEX PROBLEMS: Use research-based knowledge and
research methods including design of experiments, analysis and interpretation of data, and synthesis of the
information to provide valid conclusions.
PO5: MODERN TOOL USAGE: Create, select, and apply appropriate techniques, resources, and modern
engineering and IT tools including prediction and modeling to complex engineering activities with an
understanding of the limitations.
PO6: THE ENGINEER AND SOCIETY: Apply reasoning informed by the contextual knowledge to assess
societal, health, safety, legal and cultural issues and the consequent responsibilities relevant to the professional
engineering practice.
PO7: ENVIRONMENT AND SUSTAINABILITY: Understand the impact of the professional engineering
solutions in societal and environmental contexts, and demonstrate the knowledge of, and need for sustainable
development.
PO8: ETHICS: Apply ethical principles and commit to professional ethics and responsibilities and norms of
the engineering practice.
PO9: INDIVIDUAL AND TEAM WORK: Function effectively as an individual, and as a member or leader in
diverse teams, and in multidisciplinary settings.
PO10: COMMUNICATION: Communicate effectively on complex engineering activities with the engineering community and with society at large, such as, being able to comprehend and write effective reports
and design documentation, make effective presentations, and give and receive clear instructions.
PO11: PROJECT MANAGAEMENT AND FINANCE: Demonstrate knowledge and understanding of the
engineering and management principles and apply these to one’s own work, as a member and leader in a team,
to manage projects and in multidisciplinary environments.
PO12: LIFE LONG LEARNING: Recognize the need for, and have the preparation and ability to engage in
independent and life-long learning in the broadest context of technological change.
COURSE OBJECTIVES
The objective of the lab is to understand the kinematics and dynamics of mechanical elements
such as linkages, gears, cams and learn to design such elements to accomplish desired
motions or tasks.
COURSE OUTCOMES
At the end of the lab sessions, the student will be able to
CO1: Understand types of motion
CO2: Analyze forces and torques of components in linkages
CO3: Understand static and dynamic balance
CO4: Understand forward and inverse kinematics of open-loop mechanisms
SL NO NAME OF THE EXPERIMENT
1 To determine the state of balance of machines for primary and
secondary forces
2 To determine the frequency of torsional vibration of a given rod
3 Determine the effect of varying mass on the centre of sleeve in
porter and proell
Governor
4 Find the motion of the follower if the given profile of the cam
5 The balance masses statically and dynamically for single rotating mass
systems
6 Determine the critical speed of a given shaft for different n-conditions
7 For a simple pendulum determine time period and its natural frequency
8
For a compound pendulum determine time period and its natural
frequency
9 Determine the effect of gyroscope for different motions
10
Determine time period, amplitude and frequency of undamped
free longitudinal vibration of spring mass system
V
ADD ON EXPERIMENTS
1 Determine the pressure distribution of lubricating oil at various load and
speed of a journal bearing
2 Determine time period, amplitude and frequency of damped free
longitudinal vibration of single degree spring mass system
V
Attainment of program outcomes & program specific outcomes
Exp.
No.
Experiment Program Outcomes
Attained
Program
Specific
Outcomes
Attained 1
PO1,PO2,PO3,PO5
PSO1,PSO2 2 To determine the frequency of torsional
vibration of a given rod
PO1,PO2,PO3,PO5
PSO1,PSO2 3 Determine the effect of varying mass
on the centre of sleeve in porter and
proell
governor
PO1,PO2,PO3,PO5
PSO1,PSO2
4 Find the motion of the follower if the
given profile of the cam
PO1,PO2,PO3,PO5
PSO1,PSO2
5 The balance masses statically and
dynamically for single rotating mass
systems
PO1,PO2,PO3,PO5
PSO1,PSO2 6 Determine the critical speed of a given
shaft for different n-conditions
PO1,PO2,PO3,PO5
PSO1,PSO2 7 For a simple pendulum determine time
period and its natural frequency
PO1,PO2,PO3,PO5
PSO1,PSO2 8 For a compound pendulum determine time
period and its natural frequency
PO1,PO2,PO3,PO5
PSO1,PSO2 9 Determine the effect of gyroscope for
different motions
PO1,PO2,PO3,PO5
PSO1,PSO2 10 Determine time period, amplitude and
frequency of undamped free
longitudinal vibration of spring mass
system
v
PO1,PO2,PO3,PO5
PSO1,PSO2
Content Beyond Syllabi
1 Determine the pressure distribution of
lubricating oil at various load and speed of
a journal bearing
PO1,PO2,PO3,PO5 PSO1,PSO2
2 Determine time period, amplitude and
frequency of damped free longitudinal
vibration of single degree spring mass
system
v
PO1,PO2,PO3,PO5 PSO1,PSO2
MAPPING COURSE OUTCOMES LEADING TO THE ACHIEVEMENT OF
PROGRAM OUTCOMES AND PROGRAM SPECIFIC OUTCOMES:
Co
urs
e
Ou
tco
me
s
Program Outcomes (PO)
PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12
CO1 3 2 2 -- 3 -- -- 3 -- -- -- --
CO2 3 2 3 -- 3 -- -- 3 -- -- -- --
CO3 3 2 3 -- 3 -- -- 3 -- -- -- --
CO4 3 3 3 -- 3 -- -- 3 -- -- -- --
CO5 3 3 1 -- 3 -- -- 3 -- -- -- --
AVG 3 2.4 2.4 -- 3 -- -- 3 -- -- -- --
Course
Outcomes
Program Specific Outcomes
(PSO)
PSO1 PSO2 PSO3
CO1 3 2 --
CO2 3 2 --
CO3 3 2 --
CO4 3 3 --
CO5 2 2 --
AVG 2.8 2.2 --
THE SIMPLE PENDULUM
Aim: To determine the natural frequency of the given simple pendulum
Apparatus required: simple pendulum, stop watch, steel rule
Theory: A pendulum is a rigid body suspended from a fixed point (hinge) which is offset
with respect to the body’s center of mass. If all the mass is assumed to be concentrated at a
point, we obtain the idealized simple pendulum. Pendulums have played an important role in
the history of dynamics. Galileo identified the pendulum as the first example of synchronous
motion, which led to the first successful clock developed by Huygens. This clock
incorporated a feedback mechanism that injected energy into the oscillations (the escapement,
a mechanism used in timepieces to control movement and to provide periodic energy
impulses to a pendulum or balance) to compensate for friction loses. In addition to horology
(the science of measuring time), pendulums have important applications in gravimetry (the
measurement of the specific gravity) and inertial navigation.
Procedure:
1. Attach the cord to the steel ball at one end, and attach the other end to the main frame,
record the length of the cord l.
2. Displace the ball from its neutral position by a small amount, and then release it to
oscillate freely .Measure and record the time T required to complete 10 oscillations
3. Adjust the cord length to a new value and repeat step-2
4. Repeat step-3 six or more times so that eight pairs of l and T are recorded 5. Replace the
steel ball with plastic ball and repeat above procedure.
Formulae used:
1. Time period T ( EXP) = t/ n
2. Time period T (THEO) = 2π√L/g
3. Frequency of theoretical f = 1 / 2π√L/g g-acceleration due to gravity ; L- length of rope in
meters
4. Frequency of experimental = 1/ T
Result:
1. To find the natural frequency of given simple pendulum f (Theo)
2. To find the natural frequency of given simple pendulum f (Exp)
COMPOUND PENDULUM
Aim: To determine the radius of gyration and mass moment of inertia of the given
rectangular rod experimentally.
Apparatus required:
1. Vertical frame
2. Rectangular rod
3. Stop watch
4. Steel rule etc
Theory:
In this experiment we shall see how the period of oscillation of a compound, or physical,
pendulum depends on the distance between the point of suspension and the centre of mass.
The compound pendulum you will use in this experiment is a one metre long bar of steel
which may be supported at different points along its length, as shown in Fig. 1.
Procedure:
1. Suspend the pendulum in the first hole by choosing the length 5 cm on the length slider.
2. Click on the lower end of the pendulum, drag it to one side through a small angle and
release it. The pendulum will begin to oscillate from side to side.
3. Repeat the process by suspending the pendulum from the remaining holes by choosing the
corresponding lengths on the length slider.
4. Draw a graph by plotting distance d along the X-axis and time period T along the Y-axis.
(A spreadsheet like Excel can be very helpful here.)
5. Calculate the average value of l/T2 for the various choices of T, and then calculate g as in
step 2 above.
6. Determine kG and IG as outlined in steps 3 and 4 above.
7. Repeat the experiment in different gravitational environments by selecting an environment
from the drop-down environment menu. If the pendulum has been oscillating, press the Stop
button to activate the environment menu.
Formulae used:
1. Time period T= t/N sec
2. Experimental time period T = 2π√((K2 + l 2 )/gl))
Where K= experimental radius of gyration l= distance from point of suspension to centre of
gravity of rod L= total length of the rod
3. Theoretical radius of gyration, Kt = L/√12 =0.2866L
4. Natural frequency fn = 1/T (Hz) and Moment of inertia Im = mk2 kg-m2
Result: The moment of inertia of the given body was determined
NATURAL FREQUENCY OF SPRING MASS SYSTEM
Aim: To determine the frequency of undamped free vibration of an equivalent spring mass
system.
Apparatus required:
1. Helical spring
2. Weight holder
3. Weights
4. Stop watch
Theory:
Spring mass system is setup used to determine the experimental frequency .the body whose
frequency is to be determine is suspended by a helical spring .When the body is moved
through a small distance along a vertical axis through the centre of gravity ,it will be
accelerate in a vertical plane. Then by taking the following readings with the single mass
system we can determine the frequency of a body. The frequency of the free vibrations is
called free or natural frequency and denoted by fn. simple pendulum is an example of
undamped free vibrations.
Procedure:
1. Measure the length of the helical spring
2. Hold the spring in the appropriate hook.
3. Connect the weight holder into the spring
4. Now apply the load in the holder
5. Spring gets start to deflection and note it down
6. Then take time for no of oscillation and note down.
7. Again repeat the experiment with different loads and find the time period 8. Calculate the
natural frequency of the system
Formulae used:
• Weight of the weight holder =1.95 kg
• Time period T= t/n sec
• Natural frequency fn = 1/T Hz
• Theoretical frequency fn = 1/(2π Hz Where K = w/δ = spring stiffness
Result: The natural frequency of the spring mass system was determined experimentally.
TORSIONAL VIBRATION OF SINGLE ROTOR SHAFT SYSTEM
AIM: To determine the natural frequency of undamped torsional vibration of a single rotor
shaft system.
Apparatus: Stop watch , vernier caliper ,steel rule
Theory:
When the particles of the shaft or disc move in a circle about the axis of the shaft, then the
vibrations are known as torsional vibrations. The shaft is twisted and untwisted alternatively
and the torsional shear stresses are induced in the shaft. Since there is no damping in the
system these are undamped vibrations. Also there is no external force is acting on the body
after giving an initial angular displacement then the body is said to be under free or natural
vibrations. Hence the given system is an undamped free torsional vibratory system.
Specifications:
Shaft diameter, d = 3 mm
Diameter of disc, D = 200 mm
Weight of the disc, W = 2.2 kg
Modulus of rigidity for shaft, C = 7.848 * 1010 N/m2
Procedure:
1. Fix the brackets at convenient position along the lower beam.
2. Grip one end of the shaft at the bracket by chuck.
3. Fix the rotor on the other end of the shaft.
4. Twist the rotor through some angle and release.
5. Note down the time required for 10 to 20 oscillations.
6. Repeat the procedure for different length of the shaft.
MODEL CALCULATION:
Polar moment of inertia of shaft = Π* d 4 / 32
Moment of inertia of disc, I = (W/g)*(D2 /8)
1. Torsional stiffness , Kt =(G*Ip)/L
Where G = modulus of rigidity of shaft = 7.848 *1010 .N/m2
2. Periodic time, T (theoretically) = 2π√I/Kt
3. Periodic time, T (expt) , T = t / n
4. Frequency, f (expt) = 1 / T
5. Frequency, f (theo) = 1/2π√I/Kt
Result:
1. The natural frequency of undamped free torsional vibration (theo)
2. The natural frequency of undamped free torsional vibration (expt)
TORSIONAL VIBRATION OF TWO ROTOR SHAFT SYSTEM
Aim: Determine the natural frequency of torsional vibration two rotor system experimentally
and compare with experimental values.
Apparatus:
1. Stop watch
2. Vernier calliper
3. Steel rule
4. Cross arms
5. Spanners
Theory:
When the particles of the shaft or disc move in a circle about the axis of the shaft, then the
vibrations are known as torsional vibrations. The shaft is twisted and untwisted alternatively
and the torsional shear stresses are induced in the shaft. Since there is no damping in the
system these are undamped vibrations. Also there is no external force is acting on the body
after giving an initial angular displacement then the body is said to be under free or natural
vibrations. Hence the given system is an undamped free torsional vibratory system.
Procedure:
1) Fix two discs A and B to the shaft and fit the shaft in the bearings.
2) Deflect the discs A and B in opposite direction by hand and release.
3) Note down time required for particular number of oscillations.
4) Fit the cross arm to one of the discs say A and attaches different masses to the ends of
cross arm and again note down time.
5) Repeat the procedure with different equal masses attached to the ends of cross arm and
note down the time.
Specifications:
1. Diameter of disc A = 200 mm
2. Diameter of disc B = 200 mm
3. Wt. of Disc A = 2.2 x9.81 N
4. Wt. of Disc B = 2.2 x 9.81 N
5. Wt. of arm (with nut and bolts) = 0.725 kg
6. Length of the cross arm = 155 gms
7. Diameter of shaft = 3mm
8. Length of shaft between rotors = L=1m
9. Additional weights
Result:
1. The natural frequency of undamped free torsional vibration (theo)
2. The natural frequency of undamped free torsional vibration (expt)
BIFILAR SUSPENSION
Aim: To determine the radius of gyration and the moment of Inertia of a given rectangular
plate
Apparatus required: Main frame, bifilar plate, weights, stopwatch, thread
Introduction:
Bifilar suspension is a disc of mass m (weight w) suspended by two vertical cords, each of
length l, from a fixed support. Each cord is symmetrically attached to the disc at the same
distance r from the mass of the disc.
Theory:
The disc is now turned through a small angle its vertical axis, the cords becomes inclined.
One being released the disc will perform oscillations about the vertical axis. At any instant
Let: ῳ = angular displacement of the disc
F = tension in each cord =w/2
Inertia torque = i × ῳ
Restoring torque = 2 × horizontal component forces of each string × r
Inertia torque = restoring torque
Formula used:
Time period T=t/N
Natural frequency fn= 1/T Hz
Radius of gyration k = (Tb/2π)√(g/L) (mm)
Where, b=distance of string from centre of gravity, T= time period
L= length of the string, N= number of oscillations
Procedure:
1. Select the bifilar plate
2. With the help of chuck tighten the string at the top.
3. Adjust the length of string to desired value with help of spirit level.
4. Give a small horizontal displacement about vertical axis.
5. Start the stop watch and note down the time required for ‘N’ oscillation.
6. Repeat the experiment by adding weights and also by changing the length of the strings.
7. Do the model calculation
Precautions & maintenance instructions:
1. Tight the drill chucks properly.
2. Length of each cord should be equal.
TRIFILAR SUSPENSION
Aim: To determine the radius of gyration of trifilar suspension.
Apparatus required: Main frame, Trifilar suspension, Bifilar plate, Weights, Stopwatch,
Thread
Introduction:
Trifilar suspension is a disc of mass m (weight w) suspended by three vertical cords, each of
length l, from a fixed support. Each cord is symmetrically attached to the disc at the same
distance r from the mass of the disc.
Theory:
The disc is now turned through a small angle its vertical axis, the cords becomes inclined.
One being released the disc will perform oscillations about the vertical axis. At any instant
Let: ѳ= angular displacement of the disc
F = tension in each cord =w/3
Inertia torque = i × ѳ
Restoring torque = 3 × horizontal component forces of each string × r
Inertia torque = restoring torque
Procedure:
1. Hang the plate from chucks with 3 strings of equal lengths at equal angular intervals
(1200each)
2. Give the plate a small twist about its polar axis
3. Measure the time taken, for 5 or 10 oscillations.
4. Repeat the experiment by changing the lengths of strings and adding weights.
TORSIONAL VIBRATION OF THE FLYWHEEL
WITH DAMPING
Aim: To determine torsional frequency of the flywheel with damping method
Equipments: Universal vibration testing machine
Description:
In this experiment, the effect of including a damper in a system undergoing torsional
Oscillations are investigated. The amount of damping in the system depends on extent to
Which the conical portion of a rotor is exposed to the viscous effects of given oil. The
Apparatus consists of a vertical shaft gripped at its upper end by a chucks attached to a
Bracket and by a similar chucks attached to a heavy rotor at its lower end. The rotor
Suspends over a transparent cylindrical container.
3) Frequency fn= 1/T Hz
FORCED VIBRATION OF A RIGID BODY – WITHOUT DAMPING
Aim: To determine of forced vibrations and to analyze all types of vibrations with its
Frequency and amplitude
Description:
When external forces act on a system during its vibratory motion, it is termed forced
vibration. Under conditions of forced vibration, the system will tend to vibrate at its own
natural frequency superimposed upon the frequency of the excitation force. Friction and
damping effects, though only slight are present in all vibrating systems; that portion of the
total amplitude not sustained by the external force will gradually decay. After a short time,
the system will vibrate at the frequency of the excitation force, regardless of the initial
conditions or natural frequency of the system. In this experiment, observe and compare the
natural frequency of the forced vibration of a rectangular section beam with the analytical
results.
Construction:
The system consists of a regular rectangular cross-section beam of mass Mb,length L , width
W and thickness t ; pinned at one end to the main frame at point O ,Where its free to rotate
about ,and suspended from point S by a linear helical spring of stiffness K at distance b from
point O.A motor with mass (M=4.55Kg ) is fitted on the beam at distance a from pivot point
O,and drives two circular discs with total eccentric mass m at distance e from the centre of
the disc (the eccentric mass is obtained from a hole in each disk with radius r and thickness
td).When the motor rotates these discs with speed ω, a harmonic excitation is established on
the beam ,and as a result of that ,the beam vibrates in the vertical plane with angle θ(t)
measured from the horizontal reference direction. The bottom of the beam carries vibrating
recorder and a pencil with a strip of paper covering it, so that you can draw vibration of the
beam for a given period of time.
Technical Specifications:
Mass of the Beam Mb = 1.120 Kg
Total length of the beam (L)= 1m
Mass of the Exciter (ma) = 4 +0.4+1.3=5.7Kg
Exciter position from one trunion end a= 525mm
Procedure:
1. Attach the vibrating recorder at suitable position with the penholder slightly pressing the
paper
2. Start the exciter motor and set at required speed and start the recorder motor
3. Now vibrations are recorded over the vibration recorder, Increase the speed and note the
vibrations
4. At the resonance speed, the amplitude of the vibrations find out
5. Hold the system and cross the speed little more than the resonance speed
6. Analyze the recorder frequency and amplitude of un-damped forced
FORCED VIBRATION OF A RIGID BODY –
SPRING SYSTEM WITH DAMPING
Aim: To determine of forced vibrations and to analyze all types of vibrations with its
frequency and amplitude
Description:
The vibration that the system executes under damping system is known as damped vibrations.
In general all the physical systems are associated with one or the other type of damping. In
certain cases amount of damping may be small in other case large. In damped vibrations there
is a reduction in amplitude over every cycle of vibration. This is due to the fact that a certain
amount of energy possessed by the vibrating system is always dissipated in overcoming
frictional resistances to the motion. The rate at which the amplitude of vibration decays
depends upon the type and amount of damping in the system. Damped vibrations can be free
vibrations or forced vibrations. Shock absorber is an example of damped vibration. Mainly
the following two aspects are important while studying damped free vibrations:
1. The frequency of damped free vibrations and
2. The rate of decay.
PROCEDURE:
• Connect the exciter to D.C. motor.
• Start the motor and allow the system to vibrate.
• Wait for 3 to 5 minutes for the amplitude to build for particular forcing frequency.
• Adjust the position of strip-chart recorder. Take the record of amplitude Vs time
on the strip-chart.
Take record by changing forcing frequency.
• Repeat the experiment for different damping. Damping can be changed adjusting the
position of the exciter.
• Plot the graph of amplitude Vs frequency for each damping condition.
Technical Specifications:
Mass of the Beam Mb = 1.120 Kg
Total length of the beam (L)= 1m
Mass of the Exciter (ma) = 4 +0.4+1.3=5.7Kg
Exciter position from one trunion end a= 525mm
BALANCING OF RECIPROCATING MASSES
Aim: To study and observe the effect of unbalanced reciprocating masses in the single
cylinder.
Apparatus required: Reciprocating balancing system, weights, etc.
Description: The Experiment of Balancing of Reciprocating masses employs variable
speed motor, Cylinder, Piston, Proximity switch with RPM Meter, variac and weights.
The Setup consists of the following
1. Base: 75 * 40 * 6 channel
2. Motor: Variable Speed Motor 0- 6000 RPM, mounted with Flange
3. Cylinder: Single Cylinder with connecting rod, piston in bearings. Crank is coupled
directly with Motor with Love-joy Coupling
4. Weights: Weights are added on piston on a bolt either axially or eccentrically to simulate
unbalance.
Provision is made from to add weight on crank in opposite direction
5. Controls: The Control consists of a variac and an RPM Meter
6. Crank weights are flats with drilled holes, 20 – 50 gms
PROCEDURE:
1. Initially remove all the weights, bolt from the system
2. Start the motor, give different speeds. Observe vibration on the system, note down the
speed.
3. Repeat it for different speeds, note them down
4. Add some weights on piston top, either eccentric or co-axial. Start the motor, fix at earlier
tested speed.
5. If Vibrations are observed, one of the following has to be done to remove the unbalance
a. Either remove some of the weights from Piston, run at tested speed and observe
b. Add weights in opposite direction of crank, run and observe vibrations at tested speed.
c. Combination of both the above
Formulae:
Angular Velocity of the crank =ω= 2 ΠN/ 60 Radians / sec
Where N is the RPM
BALANCING OF ROTATING MASSES
Aim: To balance the given rotor system dynamically with the aid of the force polygon and
the couple polygon.
Apparatus required: rotor system, weights, steel rule, etc.
Theory:
In the system of rotating masses, the rotating masses have eccentricity due to limited
accuracy in manufacturing, fitting tolerances, etc. A mass attached to a rotating shaft will
rotate with the shaft and if the centre of gravity of the rotating mass does not lie on the axis of
the shaft then the mass will be effectively rotating about an axis at certain radius equal to the
eccentricity. Since the mass has to remain at that radius, the shaft will be pulled in the
direction of the mass by a force equal to the centrifugal force due to inertia of the rotating
mass. The rotating centrifugal force provides harmonic excitation to system which thereby
causes forced vibration of the machines. We will discuss how such a force can be balanced to
remove the effect of unbalance. The unbalance is expressed as product of mass and
eccentricity.
Procedure:
1. Fix the unbalanced masses as per the given conditions: radius, angular position and plane
of masses.
Find out the balancing masses and angular positions using force polygon, and couple polygon
3. Fix the balancing masses (calculated masses) at the respective radii and angular position.
4. Run the system at certain speeds and check that the balancing is done effectively.
5. If the rotor system rotates smoothly, without considerable vibrations, means the system is
dynamically balanced.
Diagrams:
1. Plane of the masses
2. Angular position of the masses
3. Force polygon
4. Couple polygon
Result: The given rotor system has been dynamically balanced with the aid of force polygon
and couple polygon.
MOTORIZED GYROSCOPIC COUPLE APPARATUS
Aim: To analysis the gyroscopic couples and the loss of couple due to friction.
Apparatus required:
1. Gyroscope
2. Weight
3. Stopwatch
4. Proximate sensor
Theory: When a body moves along a curved path with a uniform linear velocity, a force in
the direction of centripetal acceleration(known as centripetal force) has to be applied
externally over the body, so that it moves along the required path .This external force applied
is known as active force .when a body ,itself, moving with uniform linear velocity along a
circular path ,it is subjected to the centrifugal force radially outwards. This centrifugal force
is called reactive force.
The change in angular momentum is known as active gyroscopic couple(IωωP).When the
axis of spin itself moves with angular velocity ωp, the disc is subjected to reactive couple
whose magnitude is same active couple but in opposite in direction
Procedure:
1. The disc as made to rotate at a constant speed at a specific time using variable voltage
transformer.
2. The speed of the (N) disc is measured using a tachometer or a stroboscope.
3. A weight /mass is added on the extending platform attached to the disc.
4. This causes an active gyroscopic couple and the whole assembly (rotating disc, rotor and
weight platform with weight) is standing to move in a perpendicular plane to that of plane of
rotating of disc. This is called gyroscopic motion.
5. The time taken (t) to traverse a specific angular displacement (φ=60°) is noted.
6. Calculate gyroscopic effect and compare with applied torque and find the percentage loss
in torque due to friction.
Specifications:
1. Mass of the rotor = 7kg
2. Rotor diameter =300mm
3. Rotor thickness =8 mm
4. Moment of inertia of disc couple I = MXR2/2.
5. Distance of bolt weight passing from disc centre = 23 cm.
6. Motor: Fraction HP, single phase.600rpm.
7. Autotransformer provide for speed required.
Observations:
1. Gyroscopic couple C = I *ω*ωp.N-m
Where
I -Moment of inertia of disc in kg-cm-sec2
ω-Angular velocity of precision of disc = 2πN/60 rad/sec
ωp-Angular Velocity of the precision of cycle about the Vertical (dθ/dt) in rad/sec
2. Applied couple T = W.L (N-m)
Where
W -Weight of pan in N
L -Distance of weight from center of disc (L = ----- m)
3. Percentage loss in Torque due to friction = (T-C)/T*100
Result:
Thus the gyroscopic experiment is performed and gyroscopic couple, applied torque and
percentage loss due to friction are found out.
JOURNAL BEARING APPARATUS
Aim: To find out the lubrication process and behaviour of journal bearing during lubrication
by bearing analysis apparatus
Apparatus required:
• Journal bearing
• Motor with journal bearing testing setup
• Flexible tube for measuring the pressure head of the oil
Description:
Journal bearing apparatus is designed on the basis of hydrodynamic bearing action used in
practice .In a simple journal bearing the bearing surface is bored out to a slightly larger
diameter than that of the journal .Thus, when the journal is at rest ,it makes contact with the
bearing surface along a line ,the position of which is determined by the line of action of the
external load. If the load is vertical as in fig. the line of contact is parallel to the axis of the
journal and directly below the axis. The crescent shaped space between the journal and the
bearing will be filled with lubricant. When rotation begins the first tendency is for the line of
contact to move up the bearing surface in the opposite direction to that of rotation as shown
in fig. when the journal slides over the bearing, the true reaction of the bearing on the journal
is inclined to the normal to the two surfaces at the friction angle θ, and this reaction must be
in line with load. the layer of lubricant immediately adjacent to the journal tends to be carried
round with it, but is scraped off by the bearing ,so that a condition of boundary lubrication
exists between the high spots on the journal and bearing surfaces which are actually in
contact.
Procedure:
• Fill four-liter lubricant oil in feed tank
• Release the air from the supply tube and journal with help of ball valve
• Check that some oil leakage is there for cooling
• Set the speed with help of dimmer stat and let the journal run for about 5 minutes to achieve
the steady state.
Add the required loads and keeps it horizontal position
• Note the RPM of the journal shaft
• Note pressure readings at different peripheral positions (after100 or 150) rotation of journal,
with help compound pressure gauge.
• After each reading, release pressure & take the next reading.
• Repeat the experiment for the various speeds and loads
• After the test is over set dimmer to zero position and switch off main supply.
Observations:
Diameter of the bearing (OD) = 60 mm
Diameter of the bearing (ID) = 52 mm
Shaft Diameter = 25mm
Length of the journal = 95 mm
Formula used:
1. Frictional torque
T = f*W*r N m
Coefficient friction f = 2π2 *(µN/P)*(r/c) ---------------- Pitroff’s equation
Pressure P = W/ 2rl.
2. Sommerfeld number= (r/c)2*(µN/P)
Result:
1. Determine the frictional torque
2. Draw the graph for the pressure distribution for the each load